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A271999
Halogen sequence: a(n) = A018227(n)-1.
2
1, 11, 17, 35, 53, 85, 117, 167, 217, 289, 361, 459, 557, 685, 813, 975, 1137, 1337, 1537, 1779, 2021, 2309, 2597, 2935, 3273, 3665, 4057, 4507, 4957, 5469, 5981, 6559, 7137, 7785, 8433, 9155, 9877, 10677, 11477, 12359, 13241, 14209, 15177, 16235, 17293
OFFSET
1,2
COMMENTS
Terms from 11 to 117 are the atomic numbers of the elements in group 17 in the periodic table. The elements in this group are also called halogens.
FORMULA
From Colin Barker, Nov 14 2017: (Start)
G.f.: x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2).
a(n) = (1/12)*(2*n^3 + 12*n^2 + 28*n - 12) for n>2 and even.
a(n) = (1/12)*(2*n^3 + 12*n^2 + 22*n - 24) for n>2 and odd.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8.
(End)
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 11, 17, 35, 53, 85, 117, 167}, 50] (* Paolo Xausa, Oct 21 2024 *)
PROG
(PARI) Vec(x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Nov 14 2017
CROSSREFS
Sequence in context: A086711 A039514 A098797 * A317453 A339247 A317678
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jul 02 2016
STATUS
approved